If the airline has interline agreement with KE, then you'll be able to do through-check-in, regardless you purchase tickets separately or altogether, regardless of same alliance or not. You can call both airlines and make sure. I think if the airline has interline agreement with CX, then the airline should have (pretty much) same thing with KE.

On the outbound, you have to go through customs at BOM, so you need to pick up the luggages anyway.